💡📝Dmitry Eskin wrote on Wed, Nov 30, 2016 07:40 PM UTC:
At this post I will publicate and update statistics:
Pawn = 63,0% of 1000 games (+/- 2%)
Dragon (RN, Chancellor) + pawn f = Angel (Q), 51,9% of 500 games (+/- 3%)
Phoenix (BN, Archbishop) + pawn f < Angel (Q), 46,0% of 500 games (+/- 3%)
Exchanging the Queens also affects to pawns, so the advantage of Angel may be only 75% of the full, because other 25% difference pawns gains for the better promotion.
2 Wyverns (R>1) + pawn f > 2 Griffins (R), 54,1% of 500 games (+/- 3%)
2 Pegasus (jR3) > 2 Griffins (R), 53,6% of 500 games (+/- 3%)
2 Werewolves (N+) = 2 Knights (N) + pawn f, 52,5% of 500 games (+/- 3%)
2 Unicorns (Nx) > 2 Knights (N) + pawn f, 58% of 500 games (+/- 3%)
2 Hunters (B>1) + 2 pawns f/c = 2 Monks (B), 48,1% of 500 games (+/- 3%)
2 Centaurs (jB2) < 2 Monks (B), 39,9% of 500 games (+/- 3%)
8 Fairies (px) + Phoenix (BN, Archbishop) > 8 Footmen (p) + Angel (Q), 60,2% of 100 games (+/- 3%)
7f Guards (p+) + Dragon (RN, Chancellor) < 8 Footmen (p) + Angel (Q), 42,4% of 500 games (+/- 3%)
Current equalities:
Dragon = Angel - 0.6
Phoenix = Angel - 1.0
Wyvern = Griffin - 0.3
Pegasus = Griffin + 0.2
Werewolf = Knight + 0.6
Unicorn = Knight + 0.8
Hunter = Monk - 1.1
Centaur = Monk - 0.4
Fairy = Footman + 0.2
Guard = Footman + 0.15
I think that auto statistics can't be very exact, because of experience of other strategies shows that a balance depends on player's skills and styles. The balance will be different for grandmasters and novices, for humans and engines, with openings' books and endgames' tables and without it. But it is important to ensure that the basic balance of the matchups is within acceptable limits, 40-60% rather than 70% or higher. And the automatic tests can be useful for adjusting units evaluation as provide an alternative, machine evaluation as one of the approximate marks.
So I will test separate units by 3 iterations: 100, 500 and 2500 games (200, 1000 and 5000 for basic pawn evaluating), that gives an accuracy of 0.25, 0.1 and 0.05 per unit (0.05, 0.02 and 0.01 for pawns). Then I will launch 1000 games for each match-up and 500 for mirrors. Mirrors are important to get statistics about white and black balance. All games will be launched at the minimal time limits, 1 sec per turn, because it provides greater accuracy per spent time.
At this post I will publicate and update statistics:
Pawn = 63,0% of 1000 games (+/- 2%)
Dragon (RN, Chancellor) + pawn f = Angel (Q), 51,9% of 500 games (+/- 3%)
Phoenix (BN, Archbishop) + pawn f < Angel (Q), 46,0% of 500 games (+/- 3%)
Exchanging the Queens also affects to pawns, so the advantage of Angel may be only 75% of the full, because other 25% difference pawns gains for the better promotion.
2 Wyverns (R>1) + pawn f > 2 Griffins (R), 54,1% of 500 games (+/- 3%)
2 Pegasus (jR3) > 2 Griffins (R), 53,6% of 500 games (+/- 3%)
2 Werewolves (N+) = 2 Knights (N) + pawn f, 52,5% of 500 games (+/- 3%)
2 Unicorns (Nx) > 2 Knights (N) + pawn f, 58% of 500 games (+/- 3%)
2 Hunters (B>1) + 2 pawns f/c = 2 Monks (B), 48,1% of 500 games (+/- 3%)
2 Centaurs (jB2) < 2 Monks (B), 39,9% of 500 games (+/- 3%)
8 Fairies (px) + Phoenix (BN, Archbishop) > 8 Footmen (p) + Angel (Q), 60,2% of 100 games (+/- 3%)
7f Guards (p+) + Dragon (RN, Chancellor) < 8 Footmen (p) + Angel (Q), 42,4% of 500 games (+/- 3%)
Current equalities:
Dragon = Angel - 0.6
Phoenix = Angel - 1.0
Wyvern = Griffin - 0.3
Pegasus = Griffin + 0.2
Werewolf = Knight + 0.6
Unicorn = Knight + 0.8
Hunter = Monk - 1.1
Centaur = Monk - 0.4
Fairy = Footman + 0.2
Guard = Footman + 0.15
I think that auto statistics can't be very exact, because of experience of other strategies shows that a balance depends on player's skills and styles. The balance will be different for grandmasters and novices, for humans and engines, with openings' books and endgames' tables and without it. But it is important to ensure that the basic balance of the matchups is within acceptable limits, 40-60% rather than 70% or higher. And the automatic tests can be useful for adjusting units evaluation as provide an alternative, machine evaluation as one of the approximate marks.
So I will test separate units by 3 iterations: 100, 500 and 2500 games (200, 1000 and 5000 for basic pawn evaluating), that gives an accuracy of 0.25, 0.1 and 0.05 per unit (0.05, 0.02 and 0.01 for pawns). Then I will launch 1000 games for each match-up and 500 for mirrors. Mirrors are important to get statistics about white and black balance. All games will be launched at the minimal time limits, 1 sec per turn, because it provides greater accuracy per spent time.
Overall (by the 1 iteration of test):
Hero = 3.0
Footman = 1.0
Knight = 3.25
Monk = 3.5
Griffin = 5.0
Angel = 9.5
Guard = 1.15
Centaur = 3.1
Werewolf = 3.85
Wyvern = 4.7
Dragon = 8.9
Fairy = 1.2
Hunter = 2.4
Unicorn = 4.05
Pegasus = 5.2
Phoenix = 8.5